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MIT OpenCourseWareMIT 18.02 Multivariable Calculus, Fall 2007 (2007)

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This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.

MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.


This movie is part of the collection: MIT OpenCourseWare

Producer: MIT OpenCourseWare
Audio/Visual: sound, color
Language: English
Keywords: calculus; calculus of several variables; vector algebra; determinants; matrix; matrices; vector-valued function; space motion; scalar function; partial differentiation; gradient; optimization techniques; double integrals; line integrals; exact differential; conservative fields; Green's theorem; triple integrals; surface integrals; divergence theorem Stokes' theorem; applications

Creative Commons license: Attribution-Noncommercial-Share Alike 3.0


Individual Files

Movie Files h.264 Ogg Video Real Media MPEG4
Lecture 01: Dot product. 227.3 MB 
163.8 MB 
63.0 MB 
Lecture 01: Dot product. 160.2 MB 
84.3 MB 
Lecture 02: Determinants; cross product. 310.9 MB 
223.5 MB 
86.2 MB 
Lecture 02: Determinants; cross product. 217.2 MB 
115.0 MB 
Lecture 03: Matrices; inverse matrices. 300.8 MB 
216.3 MB 
83.2 MB 
Lecture 03: Matrices; inverse matrices. 211.2 MB 
111.3 MB 
Lecture 04: Square systems; equations of planes. 288.9 MB 
202.8 MB 
79.9 MB 
Lecture 04: Square systems; equations of planes. 196.3 MB 
106.7 MB 
Lecture 05: Parametric equations for lines and curves. 299.9 MB 
213.6 MB 
82.8 MB 
Lecture 05: Parametric equations for lines and curves. 207.7 MB 
110.6 MB 
Lecture 06: Velocity, acceleration; Kepler's second law. 282.8 MB 
197.5 MB 
78.4 MB 
Lecture 06: Velocity, acceleration; Kepler's second law. 191.1 MB 
104.8 MB 
Lecture 07: Review. 293.3 MB 
205.4 MB 
81.2 MB 
Lecture 07: Review. 198.5 MB 
108.6 MB 
Lecture 08: Level curves; partial derivatives; tangent plane approximation. 272.1 MB 
163.8 MB 
75.3 MB 
Lecture 08: Level curves; partial derivatives; tangent plane approximation. 157.0 MB 
100.8 MB 
Lecture 09: Max-min problems; least squares. 292.8 MB 
200.2 MB 
81.0 MB 
Lecture 09: Max-min problems; least squares. 196.3 MB 
108.2 MB 
Lecture 10: Second derivative test; boundaries and infinity. 307.8 MB 
211.1 MB 
85.2 MB 
Lecture 10: Second derivative test; boundaries and infinity. 205.1 MB 
113.8 MB 
Lecture 11: Differentials; chain rule. 295.3 MB 
202.6 MB 
81.7 MB 
Lecture 11: Differentials; chain rule. 198.5 MB 
109.4 MB 
Lecture 12: Gradient; directional derivative; tangent plane. 295.8 MB 
190.8 MB 
81.8 MB 
Lecture 12: Gradient; directional derivative; tangent plane. 185.6 MB 
109.3 MB 
Lecture 13: Lagrange multipliers. 295.3 MB 
164.3 MB 
81.8 MB 
Lecture 13: Lagrange multipliers. 156.8 MB 
109.3 MB 
Lecture 14: Non-independent variables. 289.0 MB 
188.0 MB 
80.1 MB 
Lecture 14: Non-independent variables. 183.3 MB 
107.2 MB 
Lecture 15: Partial differential equations; review. 267.1 MB 
165.1 MB 
74.0 MB 
Lecture 15: Partial differential equations; review. 162.4 MB 
99.1 MB 
Lecture 16: Double integrals. 283.0 MB 
186.8 MB 
78.2 MB 
Lecture 16: Double integrals. 182.9 MB 
141.9 MB 
Lecture 17: Double integrals in polar coordinates; applications. 303.6 MB 
208.7 MB 
82.3 MB 
Lecture 17: Double integrals in polar coordinates; applications. 206.7 MB 
155.4 MB 
Lecture 18: Change of variables. 293.7 MB 
193.3 MB 
79.8 MB 
Lecture 18: Change of variables. 190.3 MB 
146.5 MB 
Lecture 19: Vector fields and line integrals in the plane. 300.8 MB 
202.1 MB 
81.8 MB 
Lecture 19: Vector fields and line integrals in the plane. 200.9 MB 
154.3 MB 
Lecture 20: Path independence and conservative fields. 296.5 MB 
207.9 MB 
80.5 MB 
Lecture 20: Path independence and conservative fields. 205.3 MB 
152.9 MB 
Lecture 21: Gradient fields and potential functions. 294.8 MB 
203.2 MB 
80.2 MB 
Lecture 21: Gradient fields and potential functions. 200.6 MB 
151.8 MB 
Lecture 22: Green's theorem. 274.5 MB 
195.7 MB 
74.7 MB 
Lecture 22: Green's theorem. 191.5 MB 
141.9 MB 
Lecture 23: Flux; normal form of Green's theorem. 295.7 MB 
203.2 MB 
80.3 MB 
Lecture 23: Flux; normal form of Green's theorem. 201.5 MB 
151.9 MB 
Lecture 24: Simply connected regions; review. 288.6 MB 
205.0 MB 
78.3 MB 
Lecture 24: Simply connected regions; review. 201.0 MB 
148.9 MB 
Lecture 25: Triple integrals in rectangular and cylindrical coordinates. 287.0 MB 
203.2 MB 
77.8 MB 
Lecture 25: Triple integrals in rectangular and cylindrical coordinates. 200.1 MB 
148.0 MB 
Lecture 26: Spherical coordinates; surface area. 300.5 MB 
208.1 MB 
81.6 MB 
Lecture 26: Spherical coordinates; surface area. 205.6 MB 
155.0 MB 
Lecture 27: Vector fields in 3D; surface integrals and flux. 297.4 MB 
209.7 MB 
80.8 MB 
Lecture 27: Vector fields in 3D; surface integrals and flux. 206.7 MB 
153.3 MB 
Lecture 28: Divergence theorem. 290.1 MB 
201.6 MB 
78.7 MB 
Lecture 28: Divergence theorem. 198.8 MB 
149.3 MB 
Lecture 29: Divergence theorem (cont.): applications and proof. 295.5 MB 
201.1 MB 
80.3 MB 
Lecture 29: Divergence theorem (cont.): applications and proof. 199.3 MB 
151.3 MB 
Lecture 30: Line integrals in space, curl, exactness and potentials. 292.1 MB 
195.8 MB 
79.4 MB 
Lecture 30: Line integrals in space, curl, exactness and potentials. 197.2 MB 
149.0 MB 
Lecture 31: Stokes' theorem. 284.4 MB 
184.2 MB 
78.8 MB 
Lecture 31: Stokes' theorem. 184.8 MB 
142.8 MB 
Lecture 32: Stokes' theorem (cont.); review. 295.1 MB 
204.7 MB 
81.7 MB 
Lecture 32: Stokes' theorem (cont.); review. 202.2 MB 
152.3 MB 
Lecture 33: Topological considerations; Maxwell's equations. 168.7 MB 
117.3 MB 
46.7 MB 
Lecture 33: Topological considerations; Maxwell's equations. 115.7 MB 
86.7 MB 
Lecture 34: Final review. 258.4 MB 
181.9 MB 
71.5 MB 
Lecture 34: Final review. 178.3 MB 
133.0 MB 
Lecture 35: Final review (cont.). 287.9 MB 
183.6 MB 
79.6 MB 
Lecture 35: Final review (cont.). 187.0 MB 
146.6 MB 
Image Files Thumbnail Animated GIF
Lecture 01: Dot product. 6.8 KB 
427.9 KB 
Lecture 01: Dot product. 6.3 KB 
423.6 KB 
Lecture 02: Determinants; cross product. 4.7 KB 
439.8 KB 
Lecture 02: Determinants; cross product. 4.4 KB 
433.9 KB 
Lecture 03: Matrices; inverse matrices. 5.9 KB 
430.1 KB 
Lecture 03: Matrices; inverse matrices. 5.4 KB 
427.1 KB 
Lecture 04: Square systems; equations of planes. 6.2 KB 
408.8 KB 
Lecture 04: Square systems; equations of planes. 5.9 KB 
409.2 KB 
Lecture 05: Parametric equations for lines and curves. 6.0 KB 
412.8 KB 
Lecture 05: Parametric equations for lines and curves. 5.3 KB 
410.9 KB 
Lecture 06: Velocity, acceleration; Kepler's second law. 3.7 KB 
430.9 KB 
Lecture 06: Velocity, acceleration; Kepler's second law. 3.7 KB 
426.4 KB 
Lecture 07: Review. 8.1 KB 
425.9 KB 
Lecture 07: Review. 7.2 KB 
424.5 KB 
Lecture 08: Level curves; partial derivatives; tangent plane approximation. 6.2 KB 
404.9 KB 
Lecture 08: Level curves; partial derivatives; tangent plane approximation. 5.8 KB 
410.2 KB 
Lecture 09: Max-min problems; least squares. 5.3 KB 
415.3 KB 
Lecture 09: Max-min problems; least squares. 5.2 KB 
417.7 KB 
Lecture 10: Second derivative test; boundaries and infinity. 4.6 KB 
425.7 KB 
Lecture 10: Second derivative test; boundaries and infinity. 4.2 KB 
426.0 KB 
Lecture 11: Differentials; chain rule. 5.9 KB 
430.4 KB 
Lecture 11: Differentials; chain rule. 5.6 KB 
429.5 KB 
Lecture 12: Gradient; directional derivative; tangent plane. 4.7 KB 
396.5 KB 
Lecture 12: Gradient; directional derivative; tangent plane. 4.4 KB 
394.6 KB 
Lecture 13: Lagrange multipliers. 5.8 KB 
417.6 KB 
Lecture 13: Lagrange multipliers. 5.4 KB 
415.8 KB 
Lecture 14: Non-independent variables. 4.8 KB 
409.6 KB 
Lecture 14: Non-independent variables. 4.5 KB 
406.8 KB 
Lecture 15: Partial differential equations; review. 5.7 KB 
429.2 KB 
Lecture 15: Partial differential equations; review. 5.4 KB 
432.5 KB 
Lecture 16: Double integrals. 3.6 KB 
396.1 KB 
Lecture 16: Double integrals. 3.3 KB 
401.5 KB 
Lecture 17: Double integrals in polar coordinates; applications. 5.0 KB 
416.7 KB 
Lecture 17: Double integrals in polar coordinates; applications. 4.7 KB 
417.4 KB 
Lecture 18: Change of variables. 5.0 KB 
407.2 KB 
Lecture 18: Change of variables. 4.7 KB 
404.2 KB 
Lecture 19: Vector fields and line integrals in the plane. 4.1 KB 
414.3 KB 
Lecture 19: Vector fields and line integrals in the plane. 4.2 KB 
418.5 KB 
Lecture 20: Path independence and conservative fields. 4.7 KB 
418.0 KB 
Lecture 20: Path independence and conservative fields. 4.4 KB 
417.1 KB 
Lecture 21: Gradient fields and potential functions. 4.7 KB 
418.3 KB 
Lecture 21: Gradient fields and potential functions. 4.5 KB 
413.8 KB 
Lecture 22: Green's theorem. 5.2 KB 
417.3 KB 
Lecture 22: Green's theorem. 5.1 KB 
420.7 KB 
Lecture 23: Flux; normal form of Green's theorem. 5.4 KB 
424.9 KB 
Lecture 23: Flux; normal form of Green's theorem. 5.3 KB 
428.0 KB 
Lecture 24: Simply connected regions; review. 4.3 KB 
435.7 KB 
Lecture 24: Simply connected regions; review. 5.3 KB 
434.4 KB 
Lecture 25: Triple integrals in rectangular and cylindrical coordinates. 5.0 KB 
424.3 KB 
Lecture 25: Triple integrals in rectangular and cylindrical coordinates. 5.0 KB 
424.1 KB 
Lecture 26: Spherical coordinates; surface area. 6.0 KB 
426.6 KB 
Lecture 26: Spherical coordinates; surface area. 5.6 KB 
431.0 KB 
Lecture 27: Vector fields in 3D; surface integrals and flux. 5.9 KB 
407.8 KB 
Lecture 27: Vector fields in 3D; surface integrals and flux. 5.6 KB 
404.8 KB 
Lecture 28: Divergence theorem. 5.3 KB 
425.7 KB 
Lecture 28: Divergence theorem. 5.8 KB 
427.1 KB 
Lecture 29: Divergence theorem (cont.): applications and proof. 5.3 KB 
423.4 KB 
Lecture 29: Divergence theorem (cont.): applications and proof. 5.1 KB 
422.2 KB 
Lecture 30: Line integrals in space, curl, exactness and potentials. 5.9 KB 
411.8 KB 
Lecture 30: Line integrals in space, curl, exactness and potentials. 5.9 KB 
414.5 KB 
Lecture 31: Stokes' theorem. 5.3 KB 
401.4 KB 
Lecture 31: Stokes' theorem. 5.5 KB 
410.8 KB 
Lecture 32: Stokes' theorem (cont.); review. 5.3 KB 
426.2 KB 
Lecture 32: Stokes' theorem (cont.); review. 5.1 KB 
429.9 KB 
Lecture 33: Topological considerations; Maxwell's equations. 5.6 KB 
390.9 KB 
Lecture 33: Topological considerations; Maxwell's equations. 5.4 KB 
386.9 KB 
Lecture 34: Final review. 3.8 KB 
414.0 KB 
Lecture 34: Final review. 3.6 KB 
413.4 KB 
Lecture 35: Final review (cont.). 5.8 KB 
408.8 KB 
Lecture 35: Final review (cont.). 5.8 KB 
413.7 KB 
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MIT18.02F07_reviews.xml Metadata 646.0 B 

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Reviewer: RBA713 - 5.00 out of 5 stars5.00 out of 5 stars5.00 out of 5 stars5.00 out of 5 stars5.00 out of 5 stars - June 12, 2013
Subject: Brilliant
Absolutely awesome. The amount of material covered is vast, and it goes at a million miles an hour so you need to be on your toes throughout this course. But if you go through the material thoroughly, it is totally worth it.